Gregory J. Hakim
Department of Atmospheric Sciences, University of Washington,
Seattle, WA
Journal of the Atmospheric Sciences, 57, 2951--2967.
Observationally motivated idealized initial-value problems
of cyclogenesis are studied for quasigeostrophic dynamics. The goals of
this investigation are to assess the contributions of normal-mode and non-modal
growth mechanisms and the influence of nonlinearity during incipient cyclogenesis.
The initial condition is represented by a coherent vortex superposed on
a zero-potential-vorticity parallel flow. Nonlinear solutions compare favorably
with observations, with realistic deepening of the surface cyclone, an
asymmetry in the strength of the cyclone and anticyclone, and the formation
of an upper-level front downstream from the cyclogenesis. The vortical
column of potential vorticity retains a vertical orientation in the presence
of constant vertical shear, suggesting the importance of vortex alignment.
Global energy and potential-enstrophy norms show considerably more amplification
than streamfunction variance. The growth rate of the projection onto the
most-unstable mode closely approximates the linear value during the early
stages of surface development; nonlinear effects become important after
$\approx$ 30 h, beyond which the modal-projection growth rate declines
$\approx 30$\%.
Linear solutions accurately approximate the intensity
and zonal location of the surface cyclone, as well as the asymmetry between
the cyclone and upstream anticyclone. The development of the surface cyclone
is explained, almost entirely, by the growing normal modes. The growing
normal modes also account for the development of a prominent ridge of high
pressure that forms on the tropopause downstream from the vortex. Non-modal
processes (the complementary subset to the growing normal modes) capture
the dispersion of the upper vortex, but do not contribute to deepening
the surface cyclone. The upper-level front is captured by the linear solutions,
and results from a favorable superposition between the growing normal modes
and the neutral modes. Tests reveal that surface development declines rapidly
for vortex length scales smaller than those of observed precursor disturbances.
This effect is attributed to a reduction in the vortex projection onto
the unstable normal-mode spectrum.